 Hello and welcome to this session. In this session we will discuss effect of dilation and translation on two dimensional figure using coordinates. Now a transformation changes a figure into another figure and this new figure is called the image. Now there are four methods of transforming a figure and these methods are dilation, translation, reflection and rotation. And in this session we will discuss dilation and translation. First of all let us discuss dilation. Now in this figure you can see that a triangle ABC is enlarged to form a bigger triangle A double dash B double dash C double dash and the same triangle is contracted to form smaller triangle A dash B dash C dash and this transformation in which the size of a figure is enlarged or reduced without changing its shape is called dilation and dilation is represented on a grid or graph paper where we can plot the coordinates and center is that point which is fixed and all points move from the fixed point at equal distances. Now here the center is the point O and then you see from front then here you can see that center of all these triangles is the point O and from here you can also see that the triangle ABC is contracted to form the triangle A dash B dash C dash and the same triangle is enlarged to form a triangle A double dash B double dash C double dash about the point O that is about the point O as the center. Here we will discuss the center at origin now if a point Pxy is on a geometrical figure now here we have taken the point Pxy as a vertex of this triangle with center origin and now we multiply each coordinate by k and if k is critical one then this is the new triangle which we will obtain and vertices of this triangle are B dash Q dash R dash each having coordinates k x k y so if k is critical one then the triangle PQR will be enlarged to a new triangle P dash Q dash R dash and if k is less than one then triangle PQR is contracted to form a triangle P double dash Q double dash R double dash each having coordinates k x k y so this is how dilation takes place when we multiply the coordinates of the vertices of a given triangle or when we multiply the coordinates of the vertices of the given geometrical figure by k and this k is called scale factor now let us discuss an example in this we have to dilate the following points by 3 now here 3 is the scale factor now we will multiply all the coordinates by 3 and we get the new coordinates as 3 3 6 12 and 9 21 first of all let us plot the original points on the graph now here we have plotted the three points now on joining these three points we get a straight line now let us plot the new points on the graph so we have plotted the three points of the graph now on joining these three points again we get a straight line now here as the scale factor is three which is greater than one so here enlargement takes place that is this blue line is enlarged to give this pink line so these three points are dilated by a scale factor of three now if we have to dilate the points by a scale factor of one upon three then here all the coordinates will be divided by three and the new coordinates will be one one two four and three seven so in this case first of all we will plot the original coordinates then on joining these points we get a straight line then we will plot the new coordinates and plotting the new coordinates again we get a straight line so in this case as the scale factor was one upon three which is less than one here this pink line is reduced to give this purple line so if scale factor is greater than one then the image is enlargement and if scale factor is less than one then image is a reduction now let us discuss the method of dilating a figure now let us discuss it with the help of an example now in this example we are given that the points m with coordinates minus three minus six g with coordinates zero nine and h with coordinates six minus nine are the vertices of triangle mgh now we have to dilate this triangle by a scale factor of one upon three to get a new triangle m dash g dash h dash now let us start with its solution here the coordinates of vertices of triangle mgh are given to us and their scale factor is one upon three so we will multiply all the coordinates by one upon three and then we get the new coordinates that is m dash as minus one minus two g dash zero three and the coordinates of h dash will be two minus three now first of all let us plot the vertices mgh on the graph so we have plotted all the three vertices on the graph now joining these three vertices we get the triangle mgh now let us plot the new vertices on the graph so we have plotted the new vertices on the graph and on joining the new vertices we get the new triangle m dash g dash h dash so here the figure mgh is reduced to give a new figure m dash g dash h dash and now we discuss translation now in this figure you can see the two triangles are similar in size and shape it just seems that the triangle is slided to another position and this is called translation now a translation is a transformation in which a figure slides but does not turn and every point of the figure moves the same distance and in the same direction and the original figure and its image have same size and shape so here the triangle a and triangle a dash are having same size and shape now in this figure these two triangles have same shape but the size of these two triangles is different so this is not a translation now let us discuss the method of showing translation of a geometrical figure on a graph paper now consider an example in this triangle a b c has vertices a b and c that is the vertex a with coordinates minus 2 1 vertex b with coordinates 2 5 and vertex c with coordinates 1 2 now we have to translate this triangle three units right and three units down now in translation for obtaining the new coordinates we will add and subtract the units from original coordinate depending on translating units right left up or down now left and right movement leaves to change in x coordinate up and down movement leaves to change in y coordinate for moving up we add in the y coordinate for moving down we subtract in the y coordinate for moving right we add in the x coordinate and for moving left we subtract in the x coordinate now here we have to move three units right it means we have to add three to the x coordinates and we have to move three units down it means we have to subtract three from the y coordinate of the vertices a b and c so here we have drawn a table in the first column we have written the original vertices and in the last column we will find the new vertices after translation now add in three to the x coordinate and subtracting three from the y coordinate of vertex a we get the new vertex a dash whose coordinates are one minus two similarly we get the new vertices b dash c dash now first of all we will plot the points a b and c on the graph and join them so here we have plotted the points a b and c and on joining them we get a triangle a b c now we will plot the new vertices on the graph so here we have plotted the points a dash b dash c dash on the graph now on joining these points we get the new triangle a dash b dash c dash now from the graph you can see that the point b has moved to b dash by moving three units right and then three units down similarly the point c has moved to c dash and point a has moved to a dash so this new image a dash b dash c dash is formed by translation so in this session we have learned about the effect of dilation and translation on two dimensional figure using coordinates and this completes our session hope you all have enjoyed the session